a. What are the mean and standard deviation of the number of online retail orders that turn out to be fraudulent? The mean number of online retail orders that turn out to be fraudulent is 1.4 . (Type an integer or a decimal. Round to four decimal places as needed.) The standard deviation of the number of fraudulent retail orders is 1.141 . (Type an integer or a decimal. Round to three decimal places as needed.) b. What is the probability that zero online retail orders will turn out to be fraudulent? 0.2342 (Type an integer or a decimal. Round to four decimal places as needed.) c. What is the probability that one online retail order will turn out to be fraudulent? 0.3526 (Type an integer or a decimal. Round to four decimal places as needed.) d. What is the probability that two or more online retail orders will turn out to be fraudulent? (Type an integer or a decimal. Round to four decimal places as needed.)
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Given that the mean number of fraudulent retail orders is 1.4, we can use the Poisson distribution formula to calculate the probability of zero fraudulent orders: \[ P(X=0) = \frac{e^{-1.4} \times 1.4^0}{0!} \] \[ P(X=0) = e^{-1.4} \] \[ P(X=0) = 0.2466 \] Show more…
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The Sampling Distribution of the Sample Mean
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